Sheet material dispensers made of plastic material and which in use rest upon an underlying surface are known. The dispenser of the present invention, however, is intended to be mounted on an upright wall and in cantilevered relation thereto. This imposes considerable stress on the plastic walls of the dispenser, particularly when the dispenser is carrying the weight of its contents and the contents are dispensed through a dispensing slot, thus subjecting the dispenser to twisting forces which tend to distort the dispenser and impose stress upon the latches which hold hollow base and cover portions of the dispenser together. The stress imposed upon the dispenser by dispensing sheet material is particularly acute when the sheet material comprises a relatively non-yieldable and non-tearable material such as plastic film used in plastic bags, such as trash bags, garbage bags, food containing bags, etc. Such stress is further increased if the sheet material is pulled out of the dispenser with a sideways motion, thus tending to twist the dispenser.